Polytope of Type {30,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,4}*720
if this polytope has a name.
Group : SmallGroup(720,784)
Rank : 3
Schlafli Type : {30,4}
Number of vertices, edges, etc : 90, 180, 12
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {30,4,2} of size 1440
Vertex Figure Of :
   {2,30,4} of size 1440
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {6,4}*144
   9-fold quotients : {10,4}*80
   10-fold quotients : {6,4}*72
   18-fold quotients : {10,2}*40
   36-fold quotients : {5,2}*20
   45-fold quotients : {2,4}*16
   90-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {60,4}*1440, {30,8}*1440
Permutation Representation (GAP) :

s0 := ( 2, 5)( 3, 4)( 6,11)( 7,15)( 8,14)( 9,13)(10,12)(16,31)(17,35)(18,34)
(19,33)(20,32)(21,41)(22,45)(23,44)(24,43)(25,42)(26,36)(27,40)(28,39)(29,38)
(30,37);;
s1 := ( 1,17)( 2,16)( 3,20)( 4,19)( 5,18)( 6, 7)( 8,10)(11,42)(12,41)(13,45)
(14,44)(15,43)(21,37)(22,36)(23,40)(24,39)(25,38)(26,27)(28,30)(31,32)
(33,35);;
s2 := (16,41)(17,42)(18,43)(19,44)(20,45)(21,31)(22,32)(23,33)(24,34)(25,35)
(26,36)(27,37)(28,38)(29,39)(30,40);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(45)!( 2, 5)( 3, 4)( 6,11)( 7,15)( 8,14)( 9,13)(10,12)(16,31)(17,35)
(18,34)(19,33)(20,32)(21,41)(22,45)(23,44)(24,43)(25,42)(26,36)(27,40)(28,39)
(29,38)(30,37);
s1 := Sym(45)!( 1,17)( 2,16)( 3,20)( 4,19)( 5,18)( 6, 7)( 8,10)(11,42)(12,41)
(13,45)(14,44)(15,43)(21,37)(22,36)(23,40)(24,39)(25,38)(26,27)(28,30)(31,32)
(33,35);
s2 := Sym(45)!(16,41)(17,42)(18,43)(19,44)(20,45)(21,31)(22,32)(23,33)(24,34)
(25,35)(26,36)(27,37)(28,38)(29,39)(30,40);
poly := sub<Sym(45)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope